1. Sergio has a utility function ?(?1, ?2 ) = min(?1, ?2 ) where ?1 and...
1. Sergio has a utility function ?(?1, ?2 ) = min(?1, ?2 ) where ?1 and ?2 are his consumption in periods 1 and 2 respectively. Sergio earns $147 in period 1 and $63 in period 2. There is no inflation and he can borrow and save freely at an interest rate of 10%.
Calculate Sergio’s optimal level of consumption in each period. Will he save or borrow?
Homework Answers
Intertemporal BC
C1 + C2/(1+r) = Y1 + Y2/(1+r)
C1 + C2/1.1 = 147 + 63/1.1
C1 + C2/1.1 = 204.273
At eqm, C1 = C2 ( from utility function)
So, Put C1 = C2 in BC
C1 + C1/1.1 = 204.273
2.1*C1 = 224.7
C1* = C2* = 107
now in first period , as C1< Y1 , so he will save
Saving = Y1-C1
= 147 - 107
= $ 40
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